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We consider the spectrum of random Laplacian matrices of the form$$L_n=A_n-D_n$$$L_n=A_n-D_n$where$$A_n$$$A_n$is a real symmetric random matrix and$$D_n$$$D_n$is a diagonal matrix whose entries are equal to the corresponding row sums of$$A_n$$$A_n$. If$$A_n$$$A_n$is a Wigner matrix with entries in the domain of attraction of a Gaussian distribution, the empirical spectral measure of$$L_n$$$L_n$is known to converge to the free convolution of a semicircle distribution and a standard real Gaussian distribution. We consider real symmetric random matrices$$A_n$$$A_n$with independent entries (up to symmetry) whose row sums converge to a purely non-Gaussian infinitely divisible distribution, which fall into the class of Lévy–Khintchine random matrices first introduced by Jung [Trans Am Math Soc,370, (2018)]. Our main result shows that the empirical spectral measure of$$L_n$$$L_n$converges almost surely to a deterministic limit. A key step in the proof is to use the purely non-Gaussian nature of the row sums to build a random operator to which$$L_n$$$L_n$converges in an appropriate sense. This operator leads to a recursive distributional equation uniquely describing the Stieltjes transform of the limiting empirical spectral measure.

 

Using first-principles calculations, this study evaluates the structure, equation of state, and elasticity of three compositions of phase D up to 75 GPa: (1) the magnesium endmember [MgSi2O4(OH)2], (2) the aluminum endmember [Al2SiO4(OH)2], and (3) phase D with 50% Al-substitution [AlMg0.5Si1.5O4(OH)2]. We find that the Mg-endmember undergoes hydrogen-bond symmetrization and that this symmetrization is linked to a 22% increase in the bulk modulus of phase D, in agreement with previous studies. Al2SiO4(OH)2 also undergoes hydrogen-bond symmetrization, but the concomitant increase in bulk modulus is only 13%—a significant departure from the 22% increase of the Mg-endmember. Additionally, Al-endmember phase D is denser (2%–6%), less compressible (6%–25%), and has faster compressional (6%–12%) and shear velocities (12%–15%) relative to its Mg-endmember counterpart. Finally, we investigated the properties of phase D with 50% Al-substitution [AlMg0.5Si1.5O4(OH)2], and found that the hydrogen-bond symmetrization, equation of state parameters, and elastic constants of this tie-line composition cannot be accurately modeled by interpolating the properties of the Mg- and Al-endmembers. 

There is a growing body of research revealing that longitudinal passive sensing data from smartphones and wearable devices can capture daily behavior signals for human behavior modeling, such as depression detection. Most prior studies build and evaluate machine learning models using data collected from a single population. However, to ensure that a behavior model can work for a larger group of users, its generalizability needs to be verified on multiple datasets from different populations. We present the first work evaluating cross-dataset generalizability of longitudinal behavior models, using depression detection as an application. We collect multiple longitudinal passive mobile sensing datasets with over 500 users from two institutes over a two-year span, leading to four institute-year datasets. Using the datasets, we closely re-implement and evaluated nine prior depression detection algorithms. Our experiment reveals the lack of model generalizability of these methods. We also implement eight recently popular domain generalization algorithms from the machine learning community. Our results indicate that these methods also do not generalize well on our datasets, with barely any advantage over the naive baseline of guessing the majority. We then present two new algorithms with better generalizability. Our new algorithm, Reorder, significantly and consistently outperforms existing methods on most cross-dataset generalization setups. However, the overall advantage is incremental and still has great room for improvement. Our analysis reveals that the individual differences (both within and between populations) may play the most important role in the cross-dataset generalization challenge. Finally, we provide an open-source benchmark platform GLOBEM- short for Generalization of Longitudinal BEhavior Modeling - to consolidate all 19 algorithms. GLOBEM can support researchers in using, developing, and evaluating different longitudinal behavior modeling methods. We call for researchers' attention to model generalizability evaluation for future longitudinal human behavior modeling studies. 

Parasites are an integral part of coral reef ecosystems due to their influences on population dynamics, biodiversity, community structure, and food web connectivity. The Phylum Apicomplexa contains ubiquitous animal associates including the causative agents of globally important human diseases such as malaria and cryptosporidiosis. Despite their ubiquity, little is known about the biology, ecology, or distribution of these microorganisms in natural animal populations. In the US Virgin Islands, the dusky damselfish (Stegastes adustus) had a high but variable incidence of a Haemohormidium-like blood apicomplexan among 30 sites sampled. Microscopic analyses of blood smears allowed us to group these fish as infected, having low intensity infections, or uninfected. Regression analyses detected no significant differences in the condition indices (expressed as length–mass ratio). However, infection was clearly associated with potentially extremely high leukocyte counts among infected S. adustus that were not seen in uninfected fish. These results suggested the potential for some impact on the host. Linear mixed effects models indicated that S. adustus population density and meridional flow velocity were the main predictors of apicomplexan prevalence, with presence of other Stegastes species, population distance from watershed, zonal flow velocity, the complexity of the surrounding habitat, and season not showing any significant relationship with fish infection. 

Abstract Constraining the accommodation, distribution, and circulation of hydrogen in the Earth's interior is vital to our broader understanding of the deep Earth due to the significant influence of hydrogen on the material and rheological properties of minerals. Recently, a great deal of attention has been paid to the high-pressure polymorphs of FeOOH (space groups P21nm and Pnnm). These structures potentially form a hydrogen-bearing solid solution with AlOOH and phase H (MgSiO4H2) that may transport water (OH–) deep into the Earth's lower mantle. Additionally, the pyrite-type polymorph (space group Pa3 of FeOOH), and its potential dehydration have been linked to phenomena as diverse as the introduction of hydrogen into the outer core (Nishi et al. 2017), the formation of ultralow-velocity zones (ULVZs) (Liu et al. 2017), and the Great Oxidation Event (Hu et al. 2016). In this study, the high-pressure evolution of FeOOH was re-evaluated up to ~75 GPa using a combination of synchrotron-based X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), and optical absorption spectroscopy. Based on these measurements, we report three principal findings: (1) pressure-induced changes in hydrogen bonding (proton disordering or hydrogen bond symmetrization) occur at substantially lower pressures in ε-FeOOH than previously reported and are unlikely to be linked to the high-spin to low-spin transition; (2) ε-FeOOH undergoes a 10% volume collapse coincident with an isostructural Pnnm → Pnnm transition at approximately 45 GPa; and (3) a pressure-induced band gap reduction is observed in FeOOH at pressures consistent with the previously reported spin transition (40 to 50 GPa). 

A schizophrenia relapse has severe consequences for a patient’s health, work, and sometimes even life safety. If an oncoming relapse can be predicted on time, for example by detecting early behavioral changes in patients, then interventions could be provided to prevent the relapse. In this work, we investigated a machine learning based schizophrenia relapse prediction model using mobile sensing data to characterize behavioral features. A patient-independent model providing sequential predictions, closely representing the clinical deployment scenario for relapse prediction, was evaluated. The model uses the mobile sensing data from the recent four weeks to predict an oncoming relapse in the next week. We used the behavioral rhythm features extracted from daily templates of mobile sensing data, self-reported symptoms collected via EMA (Ecological Momentary Assessment), and demographics to compare different classifiers for the relapse prediction. Naive Bayes based model gave the best results with an F2 score of 0.083 when evaluated in a dataset consisting of 63 schizophrenia patients, each monitored for up to a year. The obtained F2 score, though low, is better than the baseline performance of random classification (F2 score of 0.02 ± 0.024). Thus, mobile sensing has predictive value for detecting an oncoming relapse and needs further investigation to improve the current performance. Towards that end, further feature engineering and model personalization based on the behavioral idiosyncrasies of a patient could be helpful. 

Abstract Schizophrenia is a severe and complex psychiatric disorder with heterogeneous and dynamic multi-dimensional symptoms. Behavioral rhythms, such as sleep rhythm, are usually disrupted in people with schizophrenia. As such, behavioral rhythm sensing with smartphones and machine learning can help better understand and predict their symptoms. Our goal is to predict fine-grained symptom changes with interpretable models. We computed rhythm-based features from 61 participants with 6,132 days of data and used multi-task learning to predict their ecological momentary assessment scores for 10 different symptom items. By taking into account both the similarities and differences between different participants and symptoms, our multi-task learning models perform statistically significantly better than the models trained with single-task learning for predicting patients’ individual symptom trajectories, such as feeling depressed, social, and calm and hearing voices. We also found different subtypes for each of the symptoms by applying unsupervised clustering to the feature weights in the models. Taken together, compared to the features used in the previous studies, our rhythm features not only improved models’ prediction accuracy but also provided better interpretability for how patients’ behavioral rhythms and the rhythms of their environments influence their symptom conditions. This will enable both the patients and clinicians to monitor how these factors affect a patient’s condition and how to mitigate the influence of these factors. As such, we envision that our solution allows early detection and early intervention before a patient’s condition starts deteriorating without requiring extra effort from patients and clinicians.